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Kirchhoff's Voltage & Current Laws

Gustav Robert Kirchhoff (March 12, 1824 – October 17, 1887) was a German physicist who contributed to the fundamental understanding of electrical circuits, spectroscopy, and the emission of black-body radiation by heated objects. He coined the term "black body" radiation in 1862, and two sets of independent concepts in both circuit theory and thermal emission are named "Kirchhoff's laws" after him. - Wikipedia

The concepts of Kirchhoff's Current Law and Kirchhoff's Voltage Law follow. Both assume a totally contained system where energy is conserved.

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Kirchhoff's Current (2nd) Law - RF CafeKirchhoff's Current Law

Kirchhoff's Current Law (aka Kirchhoff's 1st Law) is one of the fundamental principles in electrical circuit theory. It's named after Gustav Kirchhoff, a German physicist who formulated this law in the mid-19th century. KCL is used to analyze and describe the behavior of electric currents at junction points within electrical circuits.

The statement of Kirchhoff's Current Law is as follows:

"At any junction (or node) in an electrical circuit, the sum of the currents entering the junction is equal to the sum of the currents leaving the junction."

In other words, when you consider a point in a circuit where multiple conductors or wires meet (a node), the algebraic sum of the currents flowing into that node is always equal to the algebraic sum of the currents flowing out of that node. This law is based on the principle of conservation of electric charge, which means that no electric charge is lost or created at a junction; it simply flows in and out.

Mathematically, Kirchhoff's Current Law can be expressed as:

Σ (incoming currents) = Σ (outgoing currents)

 

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Kirchhoff's Current (2nd) Law - RF CafeKirchhoff's Voltage Law

Kirchhoff's Voltage Law (aka Kirchhoff's 2nd Law) is one of the fundamental principles in electrical circuit theory. It's named after Gustav Kirchhoff, a German physicist who formulated this law in the mid-19th century. KVL is used to analyze and describe the behavior of voltage in closed electrical circuits.

The statement of Kirchhoff's Voltage Law is as follows:

"In any closed loop or mesh within an electrical circuit, the sum of the voltage rises is equal to the sum of the voltage drops."

In other words, when you traverse a closed loop in a circuit and take into account all the voltage sources (voltage rises) and voltage-consuming elements (voltage drops) encountered along the way, the algebraic sum of these voltage changes is always zero. This is based on the conservation of energy, which states that energy cannot be created or destroyed but only transferred or transformed. In an electrical circuit, the voltage changes account for the energy transfer, and KVL ensures that no energy is lost or gained within a closed loop.

Mathematically, Kirchhoff's Voltage Law can be expressed as:

Σ (voltage rises) = Σ (voltage drops)

 

 

Posted September 8, 2023
(updated from original post on 4/26/2001)

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